A technique known as “frequency-sampling” is widely used to accommodate nonlinear wavelength tuning in swept-wavelength interferometric techniques. Swept-wavelength interferometry (SWI) is a versatile measurement technique that has found a wide range of applications, such as optical frequency domain reflectometry (OFDR), swept-wavelength optical coherence tomography (OCT) and frequency-modulated continuous-wave (FMCW) radar.
These technologies generally use the same core SWI system, namely a source of electromagnetic radiation capable of a continuous wavelength sweep and interferometer comprising a fixed reference path and a measurement path. In general, SWI systems also rely on the ability to apply a Fourier transform to the measured interference fringes. In practical systems, this Fourier transform is generally applied using the fast Fourier transform (FFT) algorithm, which imposes the requirement that data be sampled at equal intervals of the independent variable. Use of a discrete Fourier transform avoids this requirement but introduces the additional necessity that the size of each unequal interval be known. Because the independent variable of interest in swept-wavelength measurements is not time, but rather the instantaneous frequency of the electromagnetic radiation source, any nonlinearity in the tuning of the radiation wavelength renders simple time-synchronous sampling of the fringe data inadequate.
Historically, the problem of nonlinear wavelength tuning has been dealt with in three ways. One is to focus on the design and execution of a tunable radiation source with a tuning curve that is linear in time. Depending on the source, this approach can be difficult or impossible and, in general, is less convenient than the other options. Rather than linearizing the wavelength sweep, a second technique uses an auxiliary interferometer to measure the wavelength tuning rate as it changes throughout a sweep. This information is then used to resample the fringe data from a grid of equal time intervals to a grid of equal frequency intervals. The third technique, the frequency-sampling method, also uses an auxiliary interferometer, but avoids the potentially large number of interpolations required for the previous technique by using the interferometer output as a clock signal to trigger data acquisition. This method has been widely adopted because of its convenience and accuracy; however, sampling errors that result in non-uniform frequency intervals can still occur when using an interferometric clock.